Motivation
A perfectly balanced rotating object (i.e., the center of geometry and center of mass are coincident) will usually not undergo any vibration; however, due to the errors associated with geometric dimensions and the non-homogeneity of the raw material, the construction of a perfectly balanced object is difficult to achieve using a standard manufacturing process. Since it is difficult or expensive to construct a perfectly balanced object, one can expect some amount of vibration as the object rotates. This vibration can lead to performance degradation and/or a failure of the mechanical system. In addition, these undesirable vibrational effects are often accentuated during high-speed rotation. Hence, the need for control systems that provide an autobalancing capability assumes critical importance for the case of high-speed rotation-based systems where the slightest imbalance can induce very large and potentially destabilizing vibrations (e.g., precision grinding, turbines, aircraft propellers, etc.).Control Development
In this research, we address the autobalancing problem of a rotating, unbalanced disk; furthermore, we seek a solution that automatically identifies the unknown, imbalance-related parameters of the system. Specifically, we utilize Lyapunov techniques to design a nonlinear adaptive control law that regulates the disk displacement and provides angular velocity tracking. This control objective is accomplished via the application of two control forces and a control torque to the disk along with measurements of the disk's planar displacement, planar velocity, angular position, and angular velocity. The proposed controller uses a desired compensation adaptation law (DCAL) and a gain adjusted forgetting factor (GAFF) to: i) regulate disk planar vibration, ii) ensure that the disk tracks a desired angular velocity trajectory, and iii) automatically identify the unknown, imbalance-related parameters provided a mild persistency of excitation (PE) condition is satisfied. Provided this PE condition is satisfied, the control strategy achieves exponential stability whereas if the PE condition is not satisfied, the control still delivers asymptotic tracking/regulation. The work is novel in that the feedforward regression matrix is constructed to facilitate the satisfaction of the required PE condition, and the previous stability arguments regarding the GAFF have been clarified.Experimental Setup
The experimental test stand consists of the following components:- A short aluminum shaft serves as the rotor, clamped at one end to the rotating disc.
- A Slip-Ring assembly at the fixed end allows electrical connections to be passed to the rotating beam.
- A DC Motor applies the Torque to the clamped end of the beam through a pulley-transmission system.
- A Universal Joint connecting the aluminium shaft and the free end mass
- An unbalanced magneto-ferrous disk at the free-end allows the magnetic bearing to apply a control force to the rotor.
- A large air gap magnetic bearing serves as the actuator at the free end.
- A high luminosity LED is placed at the center of the magneto-ferrous disk.
- Two Linear CCD cameras are used to measure the beams free end displacement from the LED.
The controller was implemented on a Pentium 266 MHz computer running QNX, a real time operating system. The software used was Qmotor, a Graphical User interface developed in house which allows real-time control. This software has the unique ability to allow the user to change control gains without recompiling the program. The control program itself was written in C. The data aquisition was done through a MuliQ data acuisition board. Techron Linear Power Amplifiers are used to provide the current neccesary to drive the mortor and magnetic bearing assembly.
Block diagram of experimental set up
Outcome
These results have been submitted to the 2000 American Control Conference in Chicago, Illinois
